Problem: Rewrite as a simplified fraction. ${0.5\overline{80} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}1000x &= 580.808...\\ 10x &= 5.808...\end{aligned}}$ Subtracting the two equations, we have: ${990x = 575}$ ${x = \dfrac{575}{990}} $ ${x = \dfrac{115}{198}} $